A092219 Least even k such that the Euler number E(k) is divisible by prime(n), or 0 if there is no k.

0, 0, 4, 0, 0, 12, 16, 10, 0, 28, 22, 36, 40, 12, 14, 52, 0, 6, 26, 28, 72, 18, 0, 88, 96, 62, 0, 0, 108, 112, 0, 0, 42, 128, 146, 0, 156, 0, 0, 172, 0, 180, 0, 74, 196, 0, 0, 132, 0, 228, 232, 0, 210, 126, 256, 212, 268, 0, 8, 280, 0, 292, 90, 86, 312, 316, 0, 336, 0, 18, 70

Offset: 1

Author

T. D. Noe, Feb 25 2004

Keywords

• nonn

Comments

A prime p will either divide an Euler number E(k) for k < p or divide no Euler number. This sequence can be used to find A092218, primes that divide Euler numbers and A092217, primes that divide no Euler number.

Links

• T. D. Noe, Table of n, a(n) for n = 1..850
• S. S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers
• Eric Weisstein's World of Mathematics, Euler Number

Crossrefs

Cf. A000364 (Euler numbers).

Programs

Mathematica

ee=Table[Abs[EulerE[2i]], {i, 500}]; Table[p=Prime[n]; i=1; While[i<=p && Mod[ee[[i]], p]>0, i++ ]; If[i>p, 0, 2i], {n, PrimePi[500]}]